Properties

Label 8026.2.a.d.1.11
Level $8026$
Weight $2$
Character 8026.1
Self dual yes
Analytic conductor $64.088$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8026,2,Mod(1,8026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8026 = 2 \cdot 4013 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8026.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(64.0879326623\)
Analytic rank: \(0\)
Dimension: \(96\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 8026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.81326 q^{3} +1.00000 q^{4} -0.734328 q^{5} -2.81326 q^{6} -3.92682 q^{7} +1.00000 q^{8} +4.91446 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.81326 q^{3} +1.00000 q^{4} -0.734328 q^{5} -2.81326 q^{6} -3.92682 q^{7} +1.00000 q^{8} +4.91446 q^{9} -0.734328 q^{10} -2.05575 q^{11} -2.81326 q^{12} +2.59713 q^{13} -3.92682 q^{14} +2.06586 q^{15} +1.00000 q^{16} -2.17872 q^{17} +4.91446 q^{18} +2.47344 q^{19} -0.734328 q^{20} +11.0472 q^{21} -2.05575 q^{22} -7.75830 q^{23} -2.81326 q^{24} -4.46076 q^{25} +2.59713 q^{26} -5.38587 q^{27} -3.92682 q^{28} -0.714090 q^{29} +2.06586 q^{30} -6.19809 q^{31} +1.00000 q^{32} +5.78338 q^{33} -2.17872 q^{34} +2.88358 q^{35} +4.91446 q^{36} +1.58273 q^{37} +2.47344 q^{38} -7.30643 q^{39} -0.734328 q^{40} +1.17904 q^{41} +11.0472 q^{42} -2.12532 q^{43} -2.05575 q^{44} -3.60882 q^{45} -7.75830 q^{46} -6.14523 q^{47} -2.81326 q^{48} +8.41994 q^{49} -4.46076 q^{50} +6.12932 q^{51} +2.59713 q^{52} +7.69092 q^{53} -5.38587 q^{54} +1.50960 q^{55} -3.92682 q^{56} -6.95845 q^{57} -0.714090 q^{58} -5.97592 q^{59} +2.06586 q^{60} +8.67190 q^{61} -6.19809 q^{62} -19.2982 q^{63} +1.00000 q^{64} -1.90715 q^{65} +5.78338 q^{66} -0.00760682 q^{67} -2.17872 q^{68} +21.8261 q^{69} +2.88358 q^{70} -12.4138 q^{71} +4.91446 q^{72} -10.4390 q^{73} +1.58273 q^{74} +12.5493 q^{75} +2.47344 q^{76} +8.07258 q^{77} -7.30643 q^{78} +3.87181 q^{79} -0.734328 q^{80} +0.408511 q^{81} +1.17904 q^{82} -10.7691 q^{83} +11.0472 q^{84} +1.59990 q^{85} -2.12532 q^{86} +2.00892 q^{87} -2.05575 q^{88} -3.74793 q^{89} -3.60882 q^{90} -10.1985 q^{91} -7.75830 q^{92} +17.4369 q^{93} -6.14523 q^{94} -1.81632 q^{95} -2.81326 q^{96} -10.1396 q^{97} +8.41994 q^{98} -10.1029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.81326 −1.62424 −0.812119 0.583491i \(-0.801686\pi\)
−0.812119 + 0.583491i \(0.801686\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.734328 −0.328401 −0.164201 0.986427i \(-0.552504\pi\)
−0.164201 + 0.986427i \(0.552504\pi\)
\(6\) −2.81326 −1.14851
\(7\) −3.92682 −1.48420 −0.742100 0.670289i \(-0.766170\pi\)
−0.742100 + 0.670289i \(0.766170\pi\)
\(8\) 1.00000 0.353553
\(9\) 4.91446 1.63815
\(10\) −0.734328 −0.232215
\(11\) −2.05575 −0.619833 −0.309916 0.950764i \(-0.600301\pi\)
−0.309916 + 0.950764i \(0.600301\pi\)
\(12\) −2.81326 −0.812119
\(13\) 2.59713 0.720316 0.360158 0.932891i \(-0.382723\pi\)
0.360158 + 0.932891i \(0.382723\pi\)
\(14\) −3.92682 −1.04949
\(15\) 2.06586 0.533402
\(16\) 1.00000 0.250000
\(17\) −2.17872 −0.528418 −0.264209 0.964465i \(-0.585111\pi\)
−0.264209 + 0.964465i \(0.585111\pi\)
\(18\) 4.91446 1.15835
\(19\) 2.47344 0.567447 0.283723 0.958906i \(-0.408430\pi\)
0.283723 + 0.958906i \(0.408430\pi\)
\(20\) −0.734328 −0.164201
\(21\) 11.0472 2.41069
\(22\) −2.05575 −0.438288
\(23\) −7.75830 −1.61772 −0.808859 0.588003i \(-0.799914\pi\)
−0.808859 + 0.588003i \(0.799914\pi\)
\(24\) −2.81326 −0.574255
\(25\) −4.46076 −0.892153
\(26\) 2.59713 0.509340
\(27\) −5.38587 −1.03651
\(28\) −3.92682 −0.742100
\(29\) −0.714090 −0.132603 −0.0663016 0.997800i \(-0.521120\pi\)
−0.0663016 + 0.997800i \(0.521120\pi\)
\(30\) 2.06586 0.377172
\(31\) −6.19809 −1.11321 −0.556605 0.830777i \(-0.687896\pi\)
−0.556605 + 0.830777i \(0.687896\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.78338 1.00676
\(34\) −2.17872 −0.373648
\(35\) 2.88358 0.487413
\(36\) 4.91446 0.819076
\(37\) 1.58273 0.260199 0.130100 0.991501i \(-0.458470\pi\)
0.130100 + 0.991501i \(0.458470\pi\)
\(38\) 2.47344 0.401246
\(39\) −7.30643 −1.16996
\(40\) −0.734328 −0.116107
\(41\) 1.17904 0.184135 0.0920676 0.995753i \(-0.470652\pi\)
0.0920676 + 0.995753i \(0.470652\pi\)
\(42\) 11.0472 1.70462
\(43\) −2.12532 −0.324109 −0.162054 0.986782i \(-0.551812\pi\)
−0.162054 + 0.986782i \(0.551812\pi\)
\(44\) −2.05575 −0.309916
\(45\) −3.60882 −0.537971
\(46\) −7.75830 −1.14390
\(47\) −6.14523 −0.896374 −0.448187 0.893940i \(-0.647930\pi\)
−0.448187 + 0.893940i \(0.647930\pi\)
\(48\) −2.81326 −0.406060
\(49\) 8.41994 1.20285
\(50\) −4.46076 −0.630847
\(51\) 6.12932 0.858277
\(52\) 2.59713 0.360158
\(53\) 7.69092 1.05643 0.528215 0.849111i \(-0.322862\pi\)
0.528215 + 0.849111i \(0.322862\pi\)
\(54\) −5.38587 −0.732924
\(55\) 1.50960 0.203554
\(56\) −3.92682 −0.524744
\(57\) −6.95845 −0.921669
\(58\) −0.714090 −0.0937646
\(59\) −5.97592 −0.777998 −0.388999 0.921238i \(-0.627179\pi\)
−0.388999 + 0.921238i \(0.627179\pi\)
\(60\) 2.06586 0.266701
\(61\) 8.67190 1.11032 0.555161 0.831743i \(-0.312656\pi\)
0.555161 + 0.831743i \(0.312656\pi\)
\(62\) −6.19809 −0.787159
\(63\) −19.2982 −2.43134
\(64\) 1.00000 0.125000
\(65\) −1.90715 −0.236553
\(66\) 5.78338 0.711885
\(67\) −0.00760682 −0.000929321 0 −0.000464660 1.00000i \(-0.500148\pi\)
−0.000464660 1.00000i \(0.500148\pi\)
\(68\) −2.17872 −0.264209
\(69\) 21.8261 2.62756
\(70\) 2.88358 0.344653
\(71\) −12.4138 −1.47324 −0.736622 0.676304i \(-0.763580\pi\)
−0.736622 + 0.676304i \(0.763580\pi\)
\(72\) 4.91446 0.579174
\(73\) −10.4390 −1.22180 −0.610898 0.791709i \(-0.709191\pi\)
−0.610898 + 0.791709i \(0.709191\pi\)
\(74\) 1.58273 0.183989
\(75\) 12.5493 1.44907
\(76\) 2.47344 0.283723
\(77\) 8.07258 0.919956
\(78\) −7.30643 −0.827290
\(79\) 3.87181 0.435612 0.217806 0.975992i \(-0.430110\pi\)
0.217806 + 0.975992i \(0.430110\pi\)
\(80\) −0.734328 −0.0821003
\(81\) 0.408511 0.0453902
\(82\) 1.17904 0.130203
\(83\) −10.7691 −1.18206 −0.591029 0.806651i \(-0.701278\pi\)
−0.591029 + 0.806651i \(0.701278\pi\)
\(84\) 11.0472 1.20535
\(85\) 1.59990 0.173533
\(86\) −2.12532 −0.229180
\(87\) 2.00892 0.215379
\(88\) −2.05575 −0.219144
\(89\) −3.74793 −0.397280 −0.198640 0.980073i \(-0.563652\pi\)
−0.198640 + 0.980073i \(0.563652\pi\)
\(90\) −3.60882 −0.380403
\(91\) −10.1985 −1.06909
\(92\) −7.75830 −0.808859
\(93\) 17.4369 1.80812
\(94\) −6.14523 −0.633832
\(95\) −1.81632 −0.186350
\(96\) −2.81326 −0.287128
\(97\) −10.1396 −1.02952 −0.514759 0.857335i \(-0.672119\pi\)
−0.514759 + 0.857335i \(0.672119\pi\)
\(98\) 8.41994 0.850542
\(99\) −10.1029 −1.01538
\(100\) −4.46076 −0.446076
\(101\) 9.52351 0.947624 0.473812 0.880626i \(-0.342878\pi\)
0.473812 + 0.880626i \(0.342878\pi\)
\(102\) 6.12932 0.606893
\(103\) −5.88240 −0.579610 −0.289805 0.957086i \(-0.593590\pi\)
−0.289805 + 0.957086i \(0.593590\pi\)
\(104\) 2.59713 0.254670
\(105\) −8.11226 −0.791675
\(106\) 7.69092 0.747008
\(107\) 3.55489 0.343664 0.171832 0.985126i \(-0.445031\pi\)
0.171832 + 0.985126i \(0.445031\pi\)
\(108\) −5.38587 −0.518256
\(109\) −11.2797 −1.08040 −0.540198 0.841538i \(-0.681651\pi\)
−0.540198 + 0.841538i \(0.681651\pi\)
\(110\) 1.50960 0.143934
\(111\) −4.45264 −0.422626
\(112\) −3.92682 −0.371050
\(113\) 5.24049 0.492984 0.246492 0.969145i \(-0.420722\pi\)
0.246492 + 0.969145i \(0.420722\pi\)
\(114\) −6.95845 −0.651719
\(115\) 5.69713 0.531260
\(116\) −0.714090 −0.0663016
\(117\) 12.7635 1.17999
\(118\) −5.97592 −0.550128
\(119\) 8.55546 0.784278
\(120\) 2.06586 0.188586
\(121\) −6.77388 −0.615807
\(122\) 8.67190 0.785117
\(123\) −3.31695 −0.299080
\(124\) −6.19809 −0.556605
\(125\) 6.94730 0.621385
\(126\) −19.2982 −1.71922
\(127\) −11.8477 −1.05131 −0.525656 0.850697i \(-0.676180\pi\)
−0.525656 + 0.850697i \(0.676180\pi\)
\(128\) 1.00000 0.0883883
\(129\) 5.97910 0.526430
\(130\) −1.90715 −0.167268
\(131\) 21.8323 1.90750 0.953750 0.300600i \(-0.0971869\pi\)
0.953750 + 0.300600i \(0.0971869\pi\)
\(132\) 5.78338 0.503378
\(133\) −9.71277 −0.842204
\(134\) −0.00760682 −0.000657129 0
\(135\) 3.95499 0.340392
\(136\) −2.17872 −0.186824
\(137\) −3.92644 −0.335458 −0.167729 0.985833i \(-0.553643\pi\)
−0.167729 + 0.985833i \(0.553643\pi\)
\(138\) 21.8261 1.85796
\(139\) −1.42264 −0.120667 −0.0603335 0.998178i \(-0.519216\pi\)
−0.0603335 + 0.998178i \(0.519216\pi\)
\(140\) 2.88358 0.243707
\(141\) 17.2882 1.45593
\(142\) −12.4138 −1.04174
\(143\) −5.33907 −0.446475
\(144\) 4.91446 0.409538
\(145\) 0.524376 0.0435471
\(146\) −10.4390 −0.863940
\(147\) −23.6875 −1.95371
\(148\) 1.58273 0.130100
\(149\) 17.9742 1.47250 0.736250 0.676709i \(-0.236595\pi\)
0.736250 + 0.676709i \(0.236595\pi\)
\(150\) 12.5493 1.02465
\(151\) −8.24330 −0.670830 −0.335415 0.942070i \(-0.608877\pi\)
−0.335415 + 0.942070i \(0.608877\pi\)
\(152\) 2.47344 0.200623
\(153\) −10.7072 −0.865629
\(154\) 8.07258 0.650507
\(155\) 4.55143 0.365580
\(156\) −7.30643 −0.584982
\(157\) −3.92699 −0.313408 −0.156704 0.987646i \(-0.550087\pi\)
−0.156704 + 0.987646i \(0.550087\pi\)
\(158\) 3.87181 0.308024
\(159\) −21.6366 −1.71589
\(160\) −0.734328 −0.0580537
\(161\) 30.4655 2.40102
\(162\) 0.408511 0.0320957
\(163\) 17.3602 1.35976 0.679878 0.733325i \(-0.262033\pi\)
0.679878 + 0.733325i \(0.262033\pi\)
\(164\) 1.17904 0.0920676
\(165\) −4.24689 −0.330620
\(166\) −10.7691 −0.835841
\(167\) −3.44601 −0.266660 −0.133330 0.991072i \(-0.542567\pi\)
−0.133330 + 0.991072i \(0.542567\pi\)
\(168\) 11.0472 0.852309
\(169\) −6.25489 −0.481145
\(170\) 1.59990 0.122706
\(171\) 12.1556 0.929564
\(172\) −2.12532 −0.162054
\(173\) −16.1607 −1.22868 −0.614339 0.789042i \(-0.710577\pi\)
−0.614339 + 0.789042i \(0.710577\pi\)
\(174\) 2.00892 0.152296
\(175\) 17.5166 1.32413
\(176\) −2.05575 −0.154958
\(177\) 16.8118 1.26365
\(178\) −3.74793 −0.280919
\(179\) 19.6283 1.46709 0.733545 0.679641i \(-0.237864\pi\)
0.733545 + 0.679641i \(0.237864\pi\)
\(180\) −3.60882 −0.268986
\(181\) −10.3399 −0.768559 −0.384280 0.923217i \(-0.625550\pi\)
−0.384280 + 0.923217i \(0.625550\pi\)
\(182\) −10.1985 −0.755962
\(183\) −24.3963 −1.80343
\(184\) −7.75830 −0.571949
\(185\) −1.16224 −0.0854498
\(186\) 17.4369 1.27853
\(187\) 4.47892 0.327531
\(188\) −6.14523 −0.448187
\(189\) 21.1494 1.53839
\(190\) −1.81632 −0.131770
\(191\) 17.5770 1.27183 0.635915 0.771759i \(-0.280623\pi\)
0.635915 + 0.771759i \(0.280623\pi\)
\(192\) −2.81326 −0.203030
\(193\) 5.25574 0.378316 0.189158 0.981947i \(-0.439424\pi\)
0.189158 + 0.981947i \(0.439424\pi\)
\(194\) −10.1396 −0.727979
\(195\) 5.36531 0.384218
\(196\) 8.41994 0.601424
\(197\) −8.47589 −0.603882 −0.301941 0.953327i \(-0.597635\pi\)
−0.301941 + 0.953327i \(0.597635\pi\)
\(198\) −10.1029 −0.717983
\(199\) 18.1179 1.28434 0.642171 0.766562i \(-0.278034\pi\)
0.642171 + 0.766562i \(0.278034\pi\)
\(200\) −4.46076 −0.315424
\(201\) 0.0214000 0.00150944
\(202\) 9.52351 0.670072
\(203\) 2.80411 0.196810
\(204\) 6.12932 0.429138
\(205\) −0.865803 −0.0604703
\(206\) −5.88240 −0.409846
\(207\) −38.1278 −2.65007
\(208\) 2.59713 0.180079
\(209\) −5.08479 −0.351722
\(210\) −8.11226 −0.559799
\(211\) −2.84303 −0.195722 −0.0978610 0.995200i \(-0.531200\pi\)
−0.0978610 + 0.995200i \(0.531200\pi\)
\(212\) 7.69092 0.528215
\(213\) 34.9232 2.39290
\(214\) 3.55489 0.243007
\(215\) 1.56068 0.106438
\(216\) −5.38587 −0.366462
\(217\) 24.3388 1.65223
\(218\) −11.2797 −0.763956
\(219\) 29.3677 1.98449
\(220\) 1.50960 0.101777
\(221\) −5.65844 −0.380628
\(222\) −4.45264 −0.298842
\(223\) −19.1545 −1.28268 −0.641339 0.767257i \(-0.721621\pi\)
−0.641339 + 0.767257i \(0.721621\pi\)
\(224\) −3.92682 −0.262372
\(225\) −21.9222 −1.46148
\(226\) 5.24049 0.348592
\(227\) 0.877514 0.0582427 0.0291213 0.999576i \(-0.490729\pi\)
0.0291213 + 0.999576i \(0.490729\pi\)
\(228\) −6.95845 −0.460835
\(229\) 27.2775 1.80255 0.901273 0.433252i \(-0.142634\pi\)
0.901273 + 0.433252i \(0.142634\pi\)
\(230\) 5.69713 0.375658
\(231\) −22.7103 −1.49423
\(232\) −0.714090 −0.0468823
\(233\) 4.79290 0.313993 0.156997 0.987599i \(-0.449819\pi\)
0.156997 + 0.987599i \(0.449819\pi\)
\(234\) 12.7635 0.834376
\(235\) 4.51261 0.294370
\(236\) −5.97592 −0.388999
\(237\) −10.8924 −0.707538
\(238\) 8.55546 0.554568
\(239\) 14.2751 0.923378 0.461689 0.887042i \(-0.347244\pi\)
0.461689 + 0.887042i \(0.347244\pi\)
\(240\) 2.06586 0.133351
\(241\) 1.24232 0.0800248 0.0400124 0.999199i \(-0.487260\pi\)
0.0400124 + 0.999199i \(0.487260\pi\)
\(242\) −6.77388 −0.435441
\(243\) 15.0084 0.962787
\(244\) 8.67190 0.555161
\(245\) −6.18300 −0.395017
\(246\) −3.31695 −0.211481
\(247\) 6.42387 0.408741
\(248\) −6.19809 −0.393579
\(249\) 30.2962 1.91994
\(250\) 6.94730 0.439386
\(251\) −21.9668 −1.38653 −0.693266 0.720682i \(-0.743829\pi\)
−0.693266 + 0.720682i \(0.743829\pi\)
\(252\) −19.2982 −1.21567
\(253\) 15.9491 1.00271
\(254\) −11.8477 −0.743390
\(255\) −4.50093 −0.281859
\(256\) 1.00000 0.0625000
\(257\) 6.00777 0.374754 0.187377 0.982288i \(-0.440001\pi\)
0.187377 + 0.982288i \(0.440001\pi\)
\(258\) 5.97910 0.372242
\(259\) −6.21511 −0.386188
\(260\) −1.90715 −0.118276
\(261\) −3.50937 −0.217224
\(262\) 21.8323 1.34881
\(263\) 26.7329 1.64842 0.824212 0.566281i \(-0.191618\pi\)
0.824212 + 0.566281i \(0.191618\pi\)
\(264\) 5.78338 0.355942
\(265\) −5.64766 −0.346933
\(266\) −9.71277 −0.595528
\(267\) 10.5439 0.645278
\(268\) −0.00760682 −0.000464660 0
\(269\) −18.4790 −1.12669 −0.563343 0.826223i \(-0.690485\pi\)
−0.563343 + 0.826223i \(0.690485\pi\)
\(270\) 3.95499 0.240693
\(271\) 27.7761 1.68728 0.843638 0.536912i \(-0.180409\pi\)
0.843638 + 0.536912i \(0.180409\pi\)
\(272\) −2.17872 −0.132104
\(273\) 28.6910 1.73646
\(274\) −3.92644 −0.237205
\(275\) 9.17023 0.552986
\(276\) 21.8261 1.31378
\(277\) −8.76025 −0.526353 −0.263176 0.964748i \(-0.584770\pi\)
−0.263176 + 0.964748i \(0.584770\pi\)
\(278\) −1.42264 −0.0853245
\(279\) −30.4603 −1.82361
\(280\) 2.88358 0.172327
\(281\) 24.5807 1.46636 0.733181 0.680034i \(-0.238035\pi\)
0.733181 + 0.680034i \(0.238035\pi\)
\(282\) 17.2882 1.02949
\(283\) 11.9549 0.710645 0.355322 0.934744i \(-0.384371\pi\)
0.355322 + 0.934744i \(0.384371\pi\)
\(284\) −12.4138 −0.736622
\(285\) 5.10978 0.302677
\(286\) −5.33907 −0.315706
\(287\) −4.62989 −0.273294
\(288\) 4.91446 0.289587
\(289\) −12.2532 −0.720775
\(290\) 0.524376 0.0307924
\(291\) 28.5253 1.67218
\(292\) −10.4390 −0.610898
\(293\) 16.6317 0.971636 0.485818 0.874060i \(-0.338522\pi\)
0.485818 + 0.874060i \(0.338522\pi\)
\(294\) −23.6875 −1.38148
\(295\) 4.38828 0.255496
\(296\) 1.58273 0.0919944
\(297\) 11.0720 0.642464
\(298\) 17.9742 1.04122
\(299\) −20.1493 −1.16527
\(300\) 12.5493 0.724534
\(301\) 8.34577 0.481042
\(302\) −8.24330 −0.474349
\(303\) −26.7921 −1.53917
\(304\) 2.47344 0.141862
\(305\) −6.36802 −0.364632
\(306\) −10.7072 −0.612092
\(307\) 26.9050 1.53555 0.767774 0.640721i \(-0.221364\pi\)
0.767774 + 0.640721i \(0.221364\pi\)
\(308\) 8.07258 0.459978
\(309\) 16.5487 0.941425
\(310\) 4.55143 0.258504
\(311\) 22.3242 1.26589 0.632943 0.774198i \(-0.281847\pi\)
0.632943 + 0.774198i \(0.281847\pi\)
\(312\) −7.30643 −0.413645
\(313\) 22.4422 1.26851 0.634254 0.773124i \(-0.281307\pi\)
0.634254 + 0.773124i \(0.281307\pi\)
\(314\) −3.92699 −0.221613
\(315\) 14.1712 0.798457
\(316\) 3.87181 0.217806
\(317\) 3.53246 0.198403 0.0992015 0.995067i \(-0.468371\pi\)
0.0992015 + 0.995067i \(0.468371\pi\)
\(318\) −21.6366 −1.21332
\(319\) 1.46799 0.0821919
\(320\) −0.734328 −0.0410502
\(321\) −10.0008 −0.558192
\(322\) 30.4655 1.69777
\(323\) −5.38895 −0.299849
\(324\) 0.408511 0.0226951
\(325\) −11.5852 −0.642631
\(326\) 17.3602 0.961493
\(327\) 31.7327 1.75482
\(328\) 1.17904 0.0651017
\(329\) 24.1312 1.33040
\(330\) −4.24689 −0.233784
\(331\) 2.89771 0.159273 0.0796364 0.996824i \(-0.474624\pi\)
0.0796364 + 0.996824i \(0.474624\pi\)
\(332\) −10.7691 −0.591029
\(333\) 7.77826 0.426246
\(334\) −3.44601 −0.188557
\(335\) 0.00558590 0.000305190 0
\(336\) 11.0472 0.602674
\(337\) 20.0941 1.09460 0.547299 0.836937i \(-0.315656\pi\)
0.547299 + 0.836937i \(0.315656\pi\)
\(338\) −6.25489 −0.340221
\(339\) −14.7429 −0.800723
\(340\) 1.59990 0.0867666
\(341\) 12.7418 0.690005
\(342\) 12.1556 0.657301
\(343\) −5.57585 −0.301068
\(344\) −2.12532 −0.114590
\(345\) −16.0275 −0.862894
\(346\) −16.1607 −0.868807
\(347\) −4.72179 −0.253479 −0.126740 0.991936i \(-0.540451\pi\)
−0.126740 + 0.991936i \(0.540451\pi\)
\(348\) 2.00892 0.107690
\(349\) 30.4172 1.62820 0.814099 0.580726i \(-0.197231\pi\)
0.814099 + 0.580726i \(0.197231\pi\)
\(350\) 17.5166 0.936303
\(351\) −13.9878 −0.746615
\(352\) −2.05575 −0.109572
\(353\) 18.0228 0.959258 0.479629 0.877471i \(-0.340771\pi\)
0.479629 + 0.877471i \(0.340771\pi\)
\(354\) 16.8118 0.893539
\(355\) 9.11578 0.483816
\(356\) −3.74793 −0.198640
\(357\) −24.0688 −1.27385
\(358\) 19.6283 1.03739
\(359\) −9.99489 −0.527510 −0.263755 0.964590i \(-0.584961\pi\)
−0.263755 + 0.964590i \(0.584961\pi\)
\(360\) −3.60882 −0.190202
\(361\) −12.8821 −0.678004
\(362\) −10.3399 −0.543454
\(363\) 19.0567 1.00022
\(364\) −10.1985 −0.534546
\(365\) 7.66567 0.401239
\(366\) −24.3963 −1.27522
\(367\) 4.60952 0.240615 0.120307 0.992737i \(-0.461612\pi\)
0.120307 + 0.992737i \(0.461612\pi\)
\(368\) −7.75830 −0.404429
\(369\) 5.79435 0.301642
\(370\) −1.16224 −0.0604222
\(371\) −30.2009 −1.56795
\(372\) 17.4369 0.904060
\(373\) −28.6127 −1.48151 −0.740754 0.671776i \(-0.765532\pi\)
−0.740754 + 0.671776i \(0.765532\pi\)
\(374\) 4.47892 0.231599
\(375\) −19.5446 −1.00928
\(376\) −6.14523 −0.316916
\(377\) −1.85459 −0.0955162
\(378\) 21.1494 1.08781
\(379\) −21.0909 −1.08337 −0.541684 0.840582i \(-0.682213\pi\)
−0.541684 + 0.840582i \(0.682213\pi\)
\(380\) −1.81632 −0.0931752
\(381\) 33.3307 1.70758
\(382\) 17.5770 0.899320
\(383\) 37.0129 1.89127 0.945635 0.325229i \(-0.105441\pi\)
0.945635 + 0.325229i \(0.105441\pi\)
\(384\) −2.81326 −0.143564
\(385\) −5.92792 −0.302115
\(386\) 5.25574 0.267510
\(387\) −10.4448 −0.530940
\(388\) −10.1396 −0.514759
\(389\) −19.9159 −1.00978 −0.504888 0.863185i \(-0.668466\pi\)
−0.504888 + 0.863185i \(0.668466\pi\)
\(390\) 5.36531 0.271683
\(391\) 16.9032 0.854831
\(392\) 8.41994 0.425271
\(393\) −61.4201 −3.09824
\(394\) −8.47589 −0.427009
\(395\) −2.84318 −0.143056
\(396\) −10.1029 −0.507690
\(397\) −23.8114 −1.19506 −0.597531 0.801846i \(-0.703852\pi\)
−0.597531 + 0.801846i \(0.703852\pi\)
\(398\) 18.1179 0.908166
\(399\) 27.3246 1.36794
\(400\) −4.46076 −0.223038
\(401\) −2.70410 −0.135036 −0.0675182 0.997718i \(-0.521508\pi\)
−0.0675182 + 0.997718i \(0.521508\pi\)
\(402\) 0.0214000 0.00106733
\(403\) −16.0973 −0.801863
\(404\) 9.52351 0.473812
\(405\) −0.299981 −0.0149062
\(406\) 2.80411 0.139165
\(407\) −3.25371 −0.161280
\(408\) 6.12932 0.303447
\(409\) 3.74277 0.185068 0.0925340 0.995710i \(-0.470503\pi\)
0.0925340 + 0.995710i \(0.470503\pi\)
\(410\) −0.865803 −0.0427589
\(411\) 11.0461 0.544865
\(412\) −5.88240 −0.289805
\(413\) 23.4664 1.15470
\(414\) −38.1278 −1.87388
\(415\) 7.90801 0.388189
\(416\) 2.59713 0.127335
\(417\) 4.00227 0.195992
\(418\) −5.08479 −0.248705
\(419\) −7.44839 −0.363878 −0.181939 0.983310i \(-0.558237\pi\)
−0.181939 + 0.983310i \(0.558237\pi\)
\(420\) −8.11226 −0.395838
\(421\) 7.08079 0.345097 0.172548 0.985001i \(-0.444800\pi\)
0.172548 + 0.985001i \(0.444800\pi\)
\(422\) −2.84303 −0.138396
\(423\) −30.2005 −1.46840
\(424\) 7.69092 0.373504
\(425\) 9.71877 0.471429
\(426\) 34.9232 1.69204
\(427\) −34.0530 −1.64794
\(428\) 3.55489 0.171832
\(429\) 15.0202 0.725183
\(430\) 1.56068 0.0752629
\(431\) −18.9658 −0.913549 −0.456775 0.889582i \(-0.650995\pi\)
−0.456775 + 0.889582i \(0.650995\pi\)
\(432\) −5.38587 −0.259128
\(433\) 12.6446 0.607659 0.303829 0.952726i \(-0.401735\pi\)
0.303829 + 0.952726i \(0.401735\pi\)
\(434\) 24.3388 1.16830
\(435\) −1.47521 −0.0707309
\(436\) −11.2797 −0.540198
\(437\) −19.1897 −0.917968
\(438\) 29.3677 1.40325
\(439\) −14.6445 −0.698946 −0.349473 0.936946i \(-0.613639\pi\)
−0.349473 + 0.936946i \(0.613639\pi\)
\(440\) 1.50960 0.0719672
\(441\) 41.3794 1.97045
\(442\) −5.65844 −0.269144
\(443\) −11.1607 −0.530260 −0.265130 0.964213i \(-0.585415\pi\)
−0.265130 + 0.964213i \(0.585415\pi\)
\(444\) −4.45264 −0.211313
\(445\) 2.75221 0.130467
\(446\) −19.1545 −0.906991
\(447\) −50.5661 −2.39169
\(448\) −3.92682 −0.185525
\(449\) 18.8977 0.891837 0.445919 0.895073i \(-0.352877\pi\)
0.445919 + 0.895073i \(0.352877\pi\)
\(450\) −21.9222 −1.03342
\(451\) −2.42382 −0.114133
\(452\) 5.24049 0.246492
\(453\) 23.1906 1.08959
\(454\) 0.877514 0.0411838
\(455\) 7.48903 0.351091
\(456\) −6.95845 −0.325859
\(457\) −15.1046 −0.706564 −0.353282 0.935517i \(-0.614934\pi\)
−0.353282 + 0.935517i \(0.614934\pi\)
\(458\) 27.2775 1.27459
\(459\) 11.7343 0.547711
\(460\) 5.69713 0.265630
\(461\) 19.7745 0.920992 0.460496 0.887662i \(-0.347672\pi\)
0.460496 + 0.887662i \(0.347672\pi\)
\(462\) −22.7103 −1.05658
\(463\) −26.8959 −1.24996 −0.624980 0.780641i \(-0.714893\pi\)
−0.624980 + 0.780641i \(0.714893\pi\)
\(464\) −0.714090 −0.0331508
\(465\) −12.8044 −0.593789
\(466\) 4.79290 0.222027
\(467\) −3.15954 −0.146206 −0.0731030 0.997324i \(-0.523290\pi\)
−0.0731030 + 0.997324i \(0.523290\pi\)
\(468\) 12.7635 0.589993
\(469\) 0.0298706 0.00137930
\(470\) 4.51261 0.208151
\(471\) 11.0477 0.509050
\(472\) −5.97592 −0.275064
\(473\) 4.36914 0.200893
\(474\) −10.8924 −0.500305
\(475\) −11.0334 −0.506249
\(476\) 8.55546 0.392139
\(477\) 37.7967 1.73059
\(478\) 14.2751 0.652927
\(479\) −2.96426 −0.135441 −0.0677203 0.997704i \(-0.521573\pi\)
−0.0677203 + 0.997704i \(0.521573\pi\)
\(480\) 2.06586 0.0942931
\(481\) 4.11057 0.187426
\(482\) 1.24232 0.0565861
\(483\) −85.7074 −3.89982
\(484\) −6.77388 −0.307904
\(485\) 7.44577 0.338095
\(486\) 15.0084 0.680793
\(487\) −3.17486 −0.143867 −0.0719334 0.997409i \(-0.522917\pi\)
−0.0719334 + 0.997409i \(0.522917\pi\)
\(488\) 8.67190 0.392558
\(489\) −48.8389 −2.20857
\(490\) −6.18300 −0.279319
\(491\) 8.43582 0.380703 0.190352 0.981716i \(-0.439037\pi\)
0.190352 + 0.981716i \(0.439037\pi\)
\(492\) −3.31695 −0.149540
\(493\) 1.55580 0.0700699
\(494\) 6.42387 0.289023
\(495\) 7.41885 0.333452
\(496\) −6.19809 −0.278303
\(497\) 48.7467 2.18659
\(498\) 30.2962 1.35760
\(499\) −27.6674 −1.23856 −0.619282 0.785169i \(-0.712576\pi\)
−0.619282 + 0.785169i \(0.712576\pi\)
\(500\) 6.94730 0.310693
\(501\) 9.69452 0.433119
\(502\) −21.9668 −0.980426
\(503\) 5.84626 0.260672 0.130336 0.991470i \(-0.458394\pi\)
0.130336 + 0.991470i \(0.458394\pi\)
\(504\) −19.2982 −0.859610
\(505\) −6.99337 −0.311201
\(506\) 15.9491 0.709026
\(507\) 17.5967 0.781495
\(508\) −11.8477 −0.525656
\(509\) −16.3150 −0.723149 −0.361575 0.932343i \(-0.617761\pi\)
−0.361575 + 0.932343i \(0.617761\pi\)
\(510\) −4.50093 −0.199305
\(511\) 40.9922 1.81339
\(512\) 1.00000 0.0441942
\(513\) −13.3216 −0.588165
\(514\) 6.00777 0.264991
\(515\) 4.31961 0.190345
\(516\) 5.97910 0.263215
\(517\) 12.6331 0.555602
\(518\) −6.21511 −0.273076
\(519\) 45.4644 1.99567
\(520\) −1.90715 −0.0836340
\(521\) −13.3369 −0.584301 −0.292151 0.956372i \(-0.594371\pi\)
−0.292151 + 0.956372i \(0.594371\pi\)
\(522\) −3.50937 −0.153601
\(523\) 21.4153 0.936426 0.468213 0.883616i \(-0.344898\pi\)
0.468213 + 0.883616i \(0.344898\pi\)
\(524\) 21.8323 0.953750
\(525\) −49.2789 −2.15071
\(526\) 26.7329 1.16561
\(527\) 13.5039 0.588240
\(528\) 5.78338 0.251689
\(529\) 37.1912 1.61701
\(530\) −5.64766 −0.245318
\(531\) −29.3684 −1.27448
\(532\) −9.71277 −0.421102
\(533\) 3.06213 0.132636
\(534\) 10.5439 0.456280
\(535\) −2.61045 −0.112860
\(536\) −0.00760682 −0.000328564 0
\(537\) −55.2197 −2.38291
\(538\) −18.4790 −0.796687
\(539\) −17.3093 −0.745565
\(540\) 3.95499 0.170196
\(541\) 9.77628 0.420315 0.210158 0.977668i \(-0.432602\pi\)
0.210158 + 0.977668i \(0.432602\pi\)
\(542\) 27.7761 1.19308
\(543\) 29.0889 1.24832
\(544\) −2.17872 −0.0934120
\(545\) 8.28298 0.354804
\(546\) 28.6910 1.22786
\(547\) −15.8470 −0.677567 −0.338783 0.940864i \(-0.610015\pi\)
−0.338783 + 0.940864i \(0.610015\pi\)
\(548\) −3.92644 −0.167729
\(549\) 42.6177 1.81888
\(550\) 9.17023 0.391020
\(551\) −1.76626 −0.0752453
\(552\) 21.8261 0.928982
\(553\) −15.2039 −0.646536
\(554\) −8.76025 −0.372187
\(555\) 3.26970 0.138791
\(556\) −1.42264 −0.0603335
\(557\) 7.25698 0.307488 0.153744 0.988111i \(-0.450867\pi\)
0.153744 + 0.988111i \(0.450867\pi\)
\(558\) −30.4603 −1.28949
\(559\) −5.51975 −0.233461
\(560\) 2.88358 0.121853
\(561\) −12.6004 −0.531988
\(562\) 24.5807 1.03687
\(563\) −0.800106 −0.0337204 −0.0168602 0.999858i \(-0.505367\pi\)
−0.0168602 + 0.999858i \(0.505367\pi\)
\(564\) 17.2882 0.727963
\(565\) −3.84824 −0.161896
\(566\) 11.9549 0.502502
\(567\) −1.60415 −0.0673681
\(568\) −12.4138 −0.520871
\(569\) −18.6311 −0.781056 −0.390528 0.920591i \(-0.627707\pi\)
−0.390528 + 0.920591i \(0.627707\pi\)
\(570\) 5.10978 0.214025
\(571\) 21.9283 0.917672 0.458836 0.888521i \(-0.348266\pi\)
0.458836 + 0.888521i \(0.348266\pi\)
\(572\) −5.33907 −0.223238
\(573\) −49.4489 −2.06576
\(574\) −4.62989 −0.193248
\(575\) 34.6079 1.44325
\(576\) 4.91446 0.204769
\(577\) 9.80941 0.408371 0.204186 0.978932i \(-0.434545\pi\)
0.204186 + 0.978932i \(0.434545\pi\)
\(578\) −12.2532 −0.509665
\(579\) −14.7858 −0.614476
\(580\) 0.524376 0.0217735
\(581\) 42.2882 1.75441
\(582\) 28.5253 1.18241
\(583\) −15.8106 −0.654810
\(584\) −10.4390 −0.431970
\(585\) −9.37260 −0.387509
\(586\) 16.6317 0.687051
\(587\) 8.51631 0.351506 0.175753 0.984434i \(-0.443764\pi\)
0.175753 + 0.984434i \(0.443764\pi\)
\(588\) −23.6875 −0.976857
\(589\) −15.3306 −0.631688
\(590\) 4.38828 0.180663
\(591\) 23.8449 0.980849
\(592\) 1.58273 0.0650499
\(593\) 4.40968 0.181084 0.0905420 0.995893i \(-0.471140\pi\)
0.0905420 + 0.995893i \(0.471140\pi\)
\(594\) 11.0720 0.454291
\(595\) −6.28251 −0.257558
\(596\) 17.9742 0.736250
\(597\) −50.9703 −2.08608
\(598\) −20.1493 −0.823968
\(599\) 20.9772 0.857104 0.428552 0.903517i \(-0.359024\pi\)
0.428552 + 0.903517i \(0.359024\pi\)
\(600\) 12.5493 0.512323
\(601\) −6.26787 −0.255672 −0.127836 0.991795i \(-0.540803\pi\)
−0.127836 + 0.991795i \(0.540803\pi\)
\(602\) 8.34577 0.340148
\(603\) −0.0373834 −0.00152237
\(604\) −8.24330 −0.335415
\(605\) 4.97425 0.202232
\(606\) −26.7921 −1.08836
\(607\) −6.78717 −0.275483 −0.137741 0.990468i \(-0.543984\pi\)
−0.137741 + 0.990468i \(0.543984\pi\)
\(608\) 2.47344 0.100311
\(609\) −7.88869 −0.319666
\(610\) −6.36802 −0.257833
\(611\) −15.9600 −0.645672
\(612\) −10.7072 −0.432814
\(613\) 22.9234 0.925866 0.462933 0.886393i \(-0.346797\pi\)
0.462933 + 0.886393i \(0.346797\pi\)
\(614\) 26.9050 1.08580
\(615\) 2.43573 0.0982182
\(616\) 8.07258 0.325254
\(617\) 5.57814 0.224568 0.112284 0.993676i \(-0.464183\pi\)
0.112284 + 0.993676i \(0.464183\pi\)
\(618\) 16.5487 0.665688
\(619\) −2.37216 −0.0953451 −0.0476726 0.998863i \(-0.515180\pi\)
−0.0476726 + 0.998863i \(0.515180\pi\)
\(620\) 4.55143 0.182790
\(621\) 41.7852 1.67678
\(622\) 22.3242 0.895117
\(623\) 14.7175 0.589643
\(624\) −7.30643 −0.292491
\(625\) 17.2022 0.688089
\(626\) 22.4422 0.896971
\(627\) 14.3049 0.571281
\(628\) −3.92699 −0.156704
\(629\) −3.44833 −0.137494
\(630\) 14.1712 0.564594
\(631\) −8.02213 −0.319356 −0.159678 0.987169i \(-0.551046\pi\)
−0.159678 + 0.987169i \(0.551046\pi\)
\(632\) 3.87181 0.154012
\(633\) 7.99819 0.317899
\(634\) 3.53246 0.140292
\(635\) 8.70008 0.345252
\(636\) −21.6366 −0.857947
\(637\) 21.8677 0.866430
\(638\) 1.46799 0.0581184
\(639\) −61.0070 −2.41340
\(640\) −0.734328 −0.0290269
\(641\) 5.33448 0.210699 0.105350 0.994435i \(-0.466404\pi\)
0.105350 + 0.994435i \(0.466404\pi\)
\(642\) −10.0008 −0.394701
\(643\) −39.1058 −1.54218 −0.771091 0.636725i \(-0.780289\pi\)
−0.771091 + 0.636725i \(0.780289\pi\)
\(644\) 30.4655 1.20051
\(645\) −4.39062 −0.172880
\(646\) −5.38895 −0.212025
\(647\) −27.0401 −1.06306 −0.531528 0.847041i \(-0.678382\pi\)
−0.531528 + 0.847041i \(0.678382\pi\)
\(648\) 0.408511 0.0160478
\(649\) 12.2850 0.482229
\(650\) −11.5852 −0.454409
\(651\) −68.4715 −2.68361
\(652\) 17.3602 0.679878
\(653\) −32.6892 −1.27923 −0.639613 0.768697i \(-0.720905\pi\)
−0.639613 + 0.768697i \(0.720905\pi\)
\(654\) 31.7327 1.24085
\(655\) −16.0321 −0.626426
\(656\) 1.17904 0.0460338
\(657\) −51.3022 −2.00149
\(658\) 24.1312 0.940734
\(659\) 22.2631 0.867248 0.433624 0.901094i \(-0.357235\pi\)
0.433624 + 0.901094i \(0.357235\pi\)
\(660\) −4.24689 −0.165310
\(661\) 21.0608 0.819169 0.409584 0.912272i \(-0.365674\pi\)
0.409584 + 0.912272i \(0.365674\pi\)
\(662\) 2.89771 0.112623
\(663\) 15.9187 0.618230
\(664\) −10.7691 −0.417920
\(665\) 7.13236 0.276581
\(666\) 7.77826 0.301402
\(667\) 5.54013 0.214515
\(668\) −3.44601 −0.133330
\(669\) 53.8866 2.08338
\(670\) 0.00558590 0.000215802 0
\(671\) −17.8273 −0.688215
\(672\) 11.0472 0.426155
\(673\) −1.31532 −0.0507020 −0.0253510 0.999679i \(-0.508070\pi\)
−0.0253510 + 0.999679i \(0.508070\pi\)
\(674\) 20.0941 0.773997
\(675\) 24.0251 0.924726
\(676\) −6.25489 −0.240573
\(677\) 27.9736 1.07511 0.537556 0.843228i \(-0.319347\pi\)
0.537556 + 0.843228i \(0.319347\pi\)
\(678\) −14.7429 −0.566197
\(679\) 39.8163 1.52801
\(680\) 1.59990 0.0613532
\(681\) −2.46868 −0.0946000
\(682\) 12.7418 0.487907
\(683\) −18.5127 −0.708369 −0.354184 0.935176i \(-0.615242\pi\)
−0.354184 + 0.935176i \(0.615242\pi\)
\(684\) 12.1556 0.464782
\(685\) 2.88329 0.110165
\(686\) −5.57585 −0.212887
\(687\) −76.7387 −2.92776
\(688\) −2.12532 −0.0810272
\(689\) 19.9744 0.760962
\(690\) −16.0275 −0.610158
\(691\) 21.3616 0.812633 0.406317 0.913732i \(-0.366813\pi\)
0.406317 + 0.913732i \(0.366813\pi\)
\(692\) −16.1607 −0.614339
\(693\) 39.6723 1.50703
\(694\) −4.72179 −0.179237
\(695\) 1.04469 0.0396272
\(696\) 2.00892 0.0761481
\(697\) −2.56880 −0.0973004
\(698\) 30.4172 1.15131
\(699\) −13.4837 −0.510000
\(700\) 17.5166 0.662066
\(701\) 4.93440 0.186370 0.0931849 0.995649i \(-0.470295\pi\)
0.0931849 + 0.995649i \(0.470295\pi\)
\(702\) −13.9878 −0.527937
\(703\) 3.91480 0.147649
\(704\) −2.05575 −0.0774791
\(705\) −12.6952 −0.478128
\(706\) 18.0228 0.678298
\(707\) −37.3971 −1.40646
\(708\) 16.8118 0.631827
\(709\) −9.37610 −0.352127 −0.176063 0.984379i \(-0.556336\pi\)
−0.176063 + 0.984379i \(0.556336\pi\)
\(710\) 9.11578 0.342109
\(711\) 19.0278 0.713599
\(712\) −3.74793 −0.140460
\(713\) 48.0867 1.80086
\(714\) −24.0688 −0.900751
\(715\) 3.92063 0.146623
\(716\) 19.6283 0.733545
\(717\) −40.1596 −1.49979
\(718\) −9.99489 −0.373006
\(719\) −14.3531 −0.535281 −0.267641 0.963519i \(-0.586244\pi\)
−0.267641 + 0.963519i \(0.586244\pi\)
\(720\) −3.60882 −0.134493
\(721\) 23.0991 0.860257
\(722\) −12.8821 −0.479421
\(723\) −3.49497 −0.129979
\(724\) −10.3399 −0.384280
\(725\) 3.18539 0.118302
\(726\) 19.0567 0.707261
\(727\) 10.3382 0.383423 0.191711 0.981451i \(-0.438596\pi\)
0.191711 + 0.981451i \(0.438596\pi\)
\(728\) −10.1985 −0.377981
\(729\) −43.4480 −1.60919
\(730\) 7.66567 0.283719
\(731\) 4.63049 0.171265
\(732\) −24.3963 −0.901715
\(733\) −2.11447 −0.0780997 −0.0390499 0.999237i \(-0.512433\pi\)
−0.0390499 + 0.999237i \(0.512433\pi\)
\(734\) 4.60952 0.170140
\(735\) 17.3944 0.641602
\(736\) −7.75830 −0.285975
\(737\) 0.0156377 0.000576024 0
\(738\) 5.79435 0.213293
\(739\) −30.1519 −1.10916 −0.554579 0.832131i \(-0.687121\pi\)
−0.554579 + 0.832131i \(0.687121\pi\)
\(740\) −1.16224 −0.0427249
\(741\) −18.0720 −0.663893
\(742\) −30.2009 −1.10871
\(743\) 9.93168 0.364358 0.182179 0.983265i \(-0.441685\pi\)
0.182179 + 0.983265i \(0.441685\pi\)
\(744\) 17.4369 0.639267
\(745\) −13.1989 −0.483571
\(746\) −28.6127 −1.04758
\(747\) −52.9240 −1.93639
\(748\) 4.47892 0.163765
\(749\) −13.9594 −0.510066
\(750\) −19.5446 −0.713668
\(751\) −15.3722 −0.560939 −0.280470 0.959863i \(-0.590490\pi\)
−0.280470 + 0.959863i \(0.590490\pi\)
\(752\) −6.14523 −0.224094
\(753\) 61.7984 2.25206
\(754\) −1.85459 −0.0675401
\(755\) 6.05328 0.220302
\(756\) 21.1494 0.769195
\(757\) −15.4552 −0.561729 −0.280864 0.959747i \(-0.590621\pi\)
−0.280864 + 0.959747i \(0.590621\pi\)
\(758\) −21.0909 −0.766057
\(759\) −44.8692 −1.62865
\(760\) −1.81632 −0.0658848
\(761\) 12.7408 0.461853 0.230927 0.972971i \(-0.425824\pi\)
0.230927 + 0.972971i \(0.425824\pi\)
\(762\) 33.3307 1.20744
\(763\) 44.2933 1.60352
\(764\) 17.5770 0.635915
\(765\) 7.86262 0.284274
\(766\) 37.0129 1.33733
\(767\) −15.5203 −0.560404
\(768\) −2.81326 −0.101515
\(769\) 46.2554 1.66801 0.834007 0.551754i \(-0.186041\pi\)
0.834007 + 0.551754i \(0.186041\pi\)
\(770\) −5.92792 −0.213627
\(771\) −16.9014 −0.608691
\(772\) 5.25574 0.189158
\(773\) 32.7888 1.17933 0.589666 0.807647i \(-0.299260\pi\)
0.589666 + 0.807647i \(0.299260\pi\)
\(774\) −10.4448 −0.375431
\(775\) 27.6482 0.993153
\(776\) −10.1396 −0.363990
\(777\) 17.4847 0.627261
\(778\) −19.9159 −0.714019
\(779\) 2.91629 0.104487
\(780\) 5.36531 0.192109
\(781\) 25.5197 0.913166
\(782\) 16.9032 0.604457
\(783\) 3.84600 0.137445
\(784\) 8.41994 0.300712
\(785\) 2.88370 0.102924
\(786\) −61.4201 −2.19078
\(787\) 31.8370 1.13487 0.567433 0.823420i \(-0.307937\pi\)
0.567433 + 0.823420i \(0.307937\pi\)
\(788\) −8.47589 −0.301941
\(789\) −75.2068 −2.67743
\(790\) −2.84318 −0.101156
\(791\) −20.5785 −0.731686
\(792\) −10.1029 −0.358991
\(793\) 22.5221 0.799783
\(794\) −23.8114 −0.845037
\(795\) 15.8883 0.563502
\(796\) 18.1179 0.642171
\(797\) −11.4111 −0.404203 −0.202101 0.979365i \(-0.564777\pi\)
−0.202101 + 0.979365i \(0.564777\pi\)
\(798\) 27.3246 0.967280
\(799\) 13.3888 0.473660
\(800\) −4.46076 −0.157712
\(801\) −18.4191 −0.650805
\(802\) −2.70410 −0.0954852
\(803\) 21.4601 0.757309
\(804\) 0.0214000 0.000754719 0
\(805\) −22.3716 −0.788497
\(806\) −16.0973 −0.567003
\(807\) 51.9863 1.83001
\(808\) 9.52351 0.335036
\(809\) −32.3923 −1.13885 −0.569426 0.822042i \(-0.692835\pi\)
−0.569426 + 0.822042i \(0.692835\pi\)
\(810\) −0.299981 −0.0105403
\(811\) 23.8988 0.839199 0.419599 0.907709i \(-0.362171\pi\)
0.419599 + 0.907709i \(0.362171\pi\)
\(812\) 2.80411 0.0984048
\(813\) −78.1414 −2.74054
\(814\) −3.25371 −0.114042
\(815\) −12.7481 −0.446546
\(816\) 6.12932 0.214569
\(817\) −5.25687 −0.183915
\(818\) 3.74277 0.130863
\(819\) −50.1200 −1.75134
\(820\) −0.865803 −0.0302351
\(821\) 13.0773 0.456402 0.228201 0.973614i \(-0.426716\pi\)
0.228201 + 0.973614i \(0.426716\pi\)
\(822\) 11.0461 0.385278
\(823\) 16.9076 0.589361 0.294680 0.955596i \(-0.404787\pi\)
0.294680 + 0.955596i \(0.404787\pi\)
\(824\) −5.88240 −0.204923
\(825\) −25.7983 −0.898181
\(826\) 23.4664 0.816499
\(827\) 1.68620 0.0586349 0.0293175 0.999570i \(-0.490667\pi\)
0.0293175 + 0.999570i \(0.490667\pi\)
\(828\) −38.1278 −1.32503
\(829\) −1.16499 −0.0404619 −0.0202309 0.999795i \(-0.506440\pi\)
−0.0202309 + 0.999795i \(0.506440\pi\)
\(830\) 7.90801 0.274491
\(831\) 24.6449 0.854922
\(832\) 2.59713 0.0900394
\(833\) −18.3447 −0.635607
\(834\) 4.00227 0.138587
\(835\) 2.53050 0.0875715
\(836\) −5.08479 −0.175861
\(837\) 33.3821 1.15386
\(838\) −7.44839 −0.257300
\(839\) 40.0136 1.38142 0.690712 0.723130i \(-0.257297\pi\)
0.690712 + 0.723130i \(0.257297\pi\)
\(840\) −8.11226 −0.279900
\(841\) −28.4901 −0.982416
\(842\) 7.08079 0.244020
\(843\) −69.1520 −2.38172
\(844\) −2.84303 −0.0978610
\(845\) 4.59314 0.158009
\(846\) −30.2005 −1.03831
\(847\) 26.5998 0.913981
\(848\) 7.69092 0.264107
\(849\) −33.6323 −1.15426
\(850\) 9.71877 0.333351
\(851\) −12.2793 −0.420929
\(852\) 34.9232 1.19645
\(853\) 18.1409 0.621133 0.310567 0.950552i \(-0.399481\pi\)
0.310567 + 0.950552i \(0.399481\pi\)
\(854\) −34.0530 −1.16527
\(855\) −8.92622 −0.305270
\(856\) 3.55489 0.121504
\(857\) −54.0968 −1.84791 −0.923956 0.382499i \(-0.875064\pi\)
−0.923956 + 0.382499i \(0.875064\pi\)
\(858\) 15.0202 0.512782
\(859\) −36.7088 −1.25249 −0.626245 0.779627i \(-0.715409\pi\)
−0.626245 + 0.779627i \(0.715409\pi\)
\(860\) 1.56068 0.0532189
\(861\) 13.0251 0.443894
\(862\) −18.9658 −0.645977
\(863\) −42.2917 −1.43963 −0.719814 0.694167i \(-0.755773\pi\)
−0.719814 + 0.694167i \(0.755773\pi\)
\(864\) −5.38587 −0.183231
\(865\) 11.8673 0.403500
\(866\) 12.6446 0.429680
\(867\) 34.4714 1.17071
\(868\) 24.3388 0.826113
\(869\) −7.95948 −0.270007
\(870\) −1.47521 −0.0500143
\(871\) −0.0197559 −0.000669404 0
\(872\) −11.2797 −0.381978
\(873\) −49.8305 −1.68651
\(874\) −19.1897 −0.649102
\(875\) −27.2808 −0.922260
\(876\) 29.3677 0.992244
\(877\) −29.1695 −0.984983 −0.492492 0.870317i \(-0.663914\pi\)
−0.492492 + 0.870317i \(0.663914\pi\)
\(878\) −14.6445 −0.494230
\(879\) −46.7895 −1.57817
\(880\) 1.50960 0.0508885
\(881\) 8.74845 0.294743 0.147371 0.989081i \(-0.452919\pi\)
0.147371 + 0.989081i \(0.452919\pi\)
\(882\) 41.3794 1.39332
\(883\) −30.6262 −1.03065 −0.515326 0.856994i \(-0.672329\pi\)
−0.515326 + 0.856994i \(0.672329\pi\)
\(884\) −5.65844 −0.190314
\(885\) −12.3454 −0.414986
\(886\) −11.1607 −0.374951
\(887\) −1.80985 −0.0607689 −0.0303845 0.999538i \(-0.509673\pi\)
−0.0303845 + 0.999538i \(0.509673\pi\)
\(888\) −4.45264 −0.149421
\(889\) 46.5238 1.56036
\(890\) 2.75221 0.0922543
\(891\) −0.839799 −0.0281343
\(892\) −19.1545 −0.641339
\(893\) −15.1999 −0.508645
\(894\) −50.5661 −1.69118
\(895\) −14.4136 −0.481794
\(896\) −3.92682 −0.131186
\(897\) 56.6854 1.89267
\(898\) 18.8977 0.630624
\(899\) 4.42600 0.147615
\(900\) −21.9222 −0.730741
\(901\) −16.7564 −0.558236
\(902\) −2.42382 −0.0807043
\(903\) −23.4789 −0.781328
\(904\) 5.24049 0.174296
\(905\) 7.59288 0.252396
\(906\) 23.1906 0.770456
\(907\) −50.9199 −1.69077 −0.845383 0.534160i \(-0.820628\pi\)
−0.845383 + 0.534160i \(0.820628\pi\)
\(908\) 0.877514 0.0291213
\(909\) 46.8029 1.55235
\(910\) 7.48903 0.248259
\(911\) −12.1154 −0.401400 −0.200700 0.979653i \(-0.564322\pi\)
−0.200700 + 0.979653i \(0.564322\pi\)
\(912\) −6.95845 −0.230417
\(913\) 22.1385 0.732678
\(914\) −15.1046 −0.499616
\(915\) 17.9149 0.592249
\(916\) 27.2775 0.901273
\(917\) −85.7317 −2.83111
\(918\) 11.7343 0.387290
\(919\) 9.90729 0.326811 0.163406 0.986559i \(-0.447752\pi\)
0.163406 + 0.986559i \(0.447752\pi\)
\(920\) 5.69713 0.187829
\(921\) −75.6908 −2.49410
\(922\) 19.7745 0.651239
\(923\) −32.2403 −1.06120
\(924\) −22.7103 −0.747114
\(925\) −7.06019 −0.232138
\(926\) −26.8959 −0.883855
\(927\) −28.9088 −0.949489
\(928\) −0.714090 −0.0234412
\(929\) 26.0654 0.855176 0.427588 0.903974i \(-0.359363\pi\)
0.427588 + 0.903974i \(0.359363\pi\)
\(930\) −12.8044 −0.419872
\(931\) 20.8262 0.682553
\(932\) 4.79290 0.156997
\(933\) −62.8038 −2.05610
\(934\) −3.15954 −0.103383
\(935\) −3.28899 −0.107562
\(936\) 12.7635 0.417188
\(937\) 2.90578 0.0949276 0.0474638 0.998873i \(-0.484886\pi\)
0.0474638 + 0.998873i \(0.484886\pi\)
\(938\) 0.0298706 0.000975310 0
\(939\) −63.1359 −2.06036
\(940\) 4.51261 0.147185
\(941\) −31.7213 −1.03408 −0.517042 0.855960i \(-0.672967\pi\)
−0.517042 + 0.855960i \(0.672967\pi\)
\(942\) 11.0477 0.359953
\(943\) −9.14735 −0.297879
\(944\) −5.97592 −0.194500
\(945\) −15.5306 −0.505209
\(946\) 4.36914 0.142053
\(947\) 45.7267 1.48592 0.742960 0.669336i \(-0.233421\pi\)
0.742960 + 0.669336i \(0.233421\pi\)
\(948\) −10.8924 −0.353769
\(949\) −27.1116 −0.880079
\(950\) −11.0334 −0.357972
\(951\) −9.93775 −0.322254
\(952\) 8.55546 0.277284
\(953\) 10.0534 0.325663 0.162832 0.986654i \(-0.447937\pi\)
0.162832 + 0.986654i \(0.447937\pi\)
\(954\) 37.7967 1.22371
\(955\) −12.9073 −0.417671
\(956\) 14.2751 0.461689
\(957\) −4.12985 −0.133499
\(958\) −2.96426 −0.0957710
\(959\) 15.4184 0.497887
\(960\) 2.06586 0.0666753
\(961\) 7.41636 0.239237
\(962\) 4.11057 0.132530
\(963\) 17.4703 0.562974
\(964\) 1.24232 0.0400124
\(965\) −3.85943 −0.124240
\(966\) −85.7074 −2.75759
\(967\) −60.1519 −1.93436 −0.967178 0.254099i \(-0.918221\pi\)
−0.967178 + 0.254099i \(0.918221\pi\)
\(968\) −6.77388 −0.217721
\(969\) 15.1605 0.487027
\(970\) 7.44577 0.239069
\(971\) 24.3630 0.781847 0.390923 0.920423i \(-0.372156\pi\)
0.390923 + 0.920423i \(0.372156\pi\)
\(972\) 15.0084 0.481393
\(973\) 5.58647 0.179094
\(974\) −3.17486 −0.101729
\(975\) 32.5922 1.04379
\(976\) 8.67190 0.277581
\(977\) −29.1378 −0.932200 −0.466100 0.884732i \(-0.654341\pi\)
−0.466100 + 0.884732i \(0.654341\pi\)
\(978\) −48.8389 −1.56169
\(979\) 7.70483 0.246247
\(980\) −6.18300 −0.197509
\(981\) −55.4335 −1.76985
\(982\) 8.43582 0.269198
\(983\) 56.2213 1.79318 0.896591 0.442860i \(-0.146036\pi\)
0.896591 + 0.442860i \(0.146036\pi\)
\(984\) −3.31695 −0.105741
\(985\) 6.22408 0.198316
\(986\) 1.55580 0.0495469
\(987\) −67.8875 −2.16088
\(988\) 6.42387 0.204370
\(989\) 16.4889 0.524316
\(990\) 7.41885 0.235786
\(991\) −16.0486 −0.509800 −0.254900 0.966967i \(-0.582043\pi\)
−0.254900 + 0.966967i \(0.582043\pi\)
\(992\) −6.19809 −0.196790
\(993\) −8.15204 −0.258697
\(994\) 48.7467 1.54615
\(995\) −13.3044 −0.421779
\(996\) 30.2962 0.959972
\(997\) 22.6280 0.716636 0.358318 0.933600i \(-0.383350\pi\)
0.358318 + 0.933600i \(0.383350\pi\)
\(998\) −27.6674 −0.875797
\(999\) −8.52439 −0.269700
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 8026.2.a.d.1.11 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8026.2.a.d.1.11 96 1.1 even 1 trivial